digpoly-curvature-measures-cnc-XY-3d.cpp

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#include <iostream>
#include <fstream>
#include <algorithm>
#include "DGtal/base/Common.h"
#include "DGtal/shapes/SurfaceMesh.h"
#include "DGtal/geometry/meshes/CorrectedNormalCurrentComputer.h"
#include "DGtal/helpers/Shortcuts.h"
#include "DGtal/helpers/ShortcutsGeometry.h"
#include "DGtal/io/writers/SurfaceMeshWriter.h"
#include "DGtal/io/colormaps/GradientColorMap.h"
#include "DGtal/io/colormaps/QuantifiedColorMap.h"
 
DGtal::GradientColorMap< double >
makeColorMap( double min_value, double max_value )
{
  DGtal::GradientColorMap< double > gradcmap( min_value, max_value );
  gradcmap.addColor( DGtal::Color( 0, 0, 255 ) );
  gradcmap.addColor( DGtal::Color( 0, 255, 255 ) );
  gradcmap.addColor( DGtal::Color( 255, 255, 255 ) );
  gradcmap.addColor( DGtal::Color( 255, 255, 0 ) );
  gradcmap.addColor( DGtal::Color( 255, 0, 0 ) );
  return gradcmap;
}
 
void usage( char* argv[] )
{
  using namespace DGtal;
  using namespace DGtal::Z3i;
  typedef Shortcuts< KSpace >          SH;
  std::cout << "Usage: " << std::endl
            << "\t" << argv[ 0 ] << " <P> <B> <h> <R> <mode>" << std::endl
            << std::endl
            << "Computation of principal curvatures and directions on"   << std::endl
            << "a digitized implicit shape using constant or "           << std::endl
            << "interpolated corrected curvature measures (based "       << std::endl
            << "on the theory of corrected normal currents)."            << std::endl
            << "- builds the surface mesh from polynomial <P>"           << std::endl
            << "- <B> defines the digitization space size [-B,B]^3"      << std::endl
            << "- <h> is the gridstep digitization"                      << std::endl
            << "- <R> is the radius of the measuring balls"              << std::endl
            << "- <mode> is either Const for constant corrected normal"  << std::endl
            << "  vector field or Interp for interpolated corrected"     << std::endl
            << "  normal vector field."                                  << std::endl
            << "It produces several OBJ files to display principal "     << std::endl
            << "curvatures and directions estimations: `example-cnc-K1.obj`" << std::endl
            << "`example-cnc-K2.obj`, `example-cnc-D1.obj`, and"         << std::endl
            << "`example-cnc-D2.obj` as well as associated MTL files."   << std::endl;
  std::cout << "You may either write your own polynomial as 3*x^2*y-z^2*x*y+1" << std::endl
            <<"or use a predefined polynomial in the following list:" << std::endl;
  auto L = SH::getPolynomialList();
  for ( const auto& p : L )
    std::cout << p.first << " : " << p.second << std::endl;
}
 
int main( int argc, char* argv[] )
{
  if ( argc <= 1 )
    {
      usage( argv );
      return 0;
    }
  using namespace DGtal;
  using namespace DGtal::Z3i;
  typedef SurfaceMesh< RealPoint, RealVector >                    SM;
  typedef CorrectedNormalCurrentComputer< RealPoint, RealVector > CNC;
  typedef Shortcuts< KSpace >          SH;
  typedef ShortcutsGeometry< KSpace > SHG;
  std::string  poly = argv[ 1 ]; // polynomial
  const double    B = argc > 2 ? atof( argv[ 2 ] ) : 1.0; // max ||_oo bbox
  const double    h = argc > 3 ? atof( argv[ 3 ] ) : 1.0; // gridstep  
  const double    R = argc > 4 ? atof( argv[ 4 ] ) : 2.0; // radius of measuring ball
  std::string  mode = argc > 5 ? argv[ 5 ] : "Const"; // either Const or Interp
  bool interpolated = mode == "Interp";
  if ( interpolated )
    std::cout << "Using vertex-*Interpolated* Corrected Normal Current" << std::endl;
  else
    std::cout << "Using face-*Constant* Corrected Normal Current" << std::endl;
  // Read polynomial and build digital surface
  auto params = SH::defaultParameters() | SHG::defaultParameters();
  params( "t-ring", 3 )( "surfaceTraversal", "Default" );
  params( "polynomial", poly )( "gridstep", h ); 
  params( "minAABB", -B )( "maxAABB", B );
  params( "offset", 3.0 );
  auto shape       = SH::makeImplicitShape3D( params );
  auto K           = SH::getKSpace( params );
  auto dshape      = SH::makeDigitizedImplicitShape3D( shape, params );
  auto bimage      = SH::makeBinaryImage( dshape, params );
  if ( bimage == nullptr ) 
    {
      trace.error() <<  "Unable to read polynomial <"
                    << poly.c_str() << ">" << std::endl;
      return 1;
    }
  auto sembedder   = SH::getSCellEmbedder( K );
  auto embedder    = SH::getCellEmbedder( K );
  auto surface     = SH::makeDigitalSurface( bimage, K, params );
  auto surfels     = SH::getSurfelRange( surface, params );
  trace.info() << "- surface has " << surfels.size()<< " surfels." << std::endl;

  SM smesh;
  std::vector< SM::Vertices > faces;
  SH::Cell2Index c2i;
  auto pointels = SH::getPointelRange( c2i, surface );
  auto vertices = SH::RealPoints( pointels.size() );
  std::transform( pointels.cbegin(), pointels.cend(), vertices.begin(),
                  [&] (const SH::Cell& c) { return h * embedder( c ); } ); 
  for ( auto&& surfel : *surface )
    {
      const auto primal_surfel_vtcs = SH::getPointelRange( K, surfel );
      SM::Vertices face;              
      for ( auto&& primal_vtx : primal_surfel_vtcs )
        face.push_back( c2i[ primal_vtx ] );
      faces.push_back( face );
    }
  smesh.init( vertices.cbegin(), vertices.cend(),
              faces.cbegin(),    faces.cend() );
  trace.info() << smesh << std::endl;

  auto exp_K1 = SHG::getFirstPrincipalCurvatures ( shape, K, surfels, params );
  auto exp_K2 = SHG::getSecondPrincipalCurvatures( shape, K, surfels, params );
  auto exp_D1 = SHG::getFirstPrincipalDirections ( shape, K, surfels, params );
  auto exp_D2 = SHG::getSecondPrincipalDirections( shape, K, surfels, params );

  // Builds a CorrectedNormalCurrentComputer object onto the SurfaceMesh object
  CNC cnc( smesh );
  // Estimates normal vectors using Convolved Trivial Normal estimator 
  auto face_normals = SHG::getCTrivialNormalVectors( surface, surfels, params );
  // Set corrected face normals => Corrected Normal Current with
  // constant per face corrected vector field.
  smesh.setFaceNormals( face_normals.cbegin(), face_normals.cend() ); // CCNC
  // Set corrected vertex normals => Corrected Normal Current with
  // smooth linearly interpolated per face corrected vector field.
  if ( interpolated ) smesh.computeVertexNormalsFromFaceNormals();    // ICNC
  // computes area, anisotropic XY curvature measures
  auto mu0  = cnc.computeMu0();
  auto muXY = cnc.computeMuXY();

  // estimates principal curvatures (K1,K2) and directions (D1,D2) by
  // measure normalization.
  std::vector< double > K1( smesh.nbFaces() );
  std::vector< double > K2( smesh.nbFaces() );
  std::vector< RealVector > D1( smesh.nbFaces() );
  std::vector< RealVector > D2( smesh.nbFaces() );
  for ( auto f = 0; f < smesh.nbFaces(); ++f )
    {
      const auto b    = smesh.faceCentroid( f );
      const auto N    = smesh.faceNormals()[ f ];
      const auto area = mu0 .measure( b, R, f );
      const auto M    = muXY.measure( b, R, f );
      std::tie( K1[ f ], K2[ f ], D1[ f ], D2[ f ] )
        = cnc.principalCurvatures( area, M, N );
    }

  auto exp_K1_min_max = std::minmax_element( exp_K1.cbegin(), exp_K1.cend() );
  auto exp_K2_min_max = std::minmax_element( exp_K2.cbegin(), exp_K2.cend() );
  auto K1_min_max = std::minmax_element( K1.cbegin(), K1.cend() );
  auto K2_min_max = std::minmax_element( K2.cbegin(), K2.cend() );
  std::cout << "Expected K1 curvatures:"
            << " min=" << *exp_K1_min_max.first << " max=" << *exp_K1_min_max.second
            << std::endl;
  std::cout << "Computed k1 curvatures:"
            << " min=" << *K1_min_max.first << " max=" << *K1_min_max.second
            << std::endl;
  std::cout << "Expected k2 curvatures:"
            << " min=" << *exp_K2_min_max.first << " max=" << *exp_K2_min_max.second
            << std::endl;
  std::cout << "Computed k2 curvatures:"
            << " min=" << *K2_min_max.first << " max=" << *K2_min_max.second
            << std::endl;
  const auto      error_K1 = SHG::getScalarsAbsoluteDifference( K1, exp_K1 );
  const auto stat_error_K1 = SHG::getStatistic( error_K1 );
  const auto   error_K1_l2 = SHG::getScalarsNormL2( K1, exp_K1 );
  trace.info() << "|K1-K1_CNC|_oo = " << stat_error_K1.max() << std::endl;
  trace.info() << "|K1-K1_CNC|_2  = " << error_K1_l2 << std::endl;
  const auto      error_K2 = SHG::getScalarsAbsoluteDifference( K2, exp_K2 );
  const auto stat_error_K2 = SHG::getStatistic( error_K2 );
  const auto   error_K2_l2 = SHG::getScalarsNormL2( K2, exp_K2 );
  trace.info() << "|K2-K2_CNC|_oo = " << stat_error_K2.max() << std::endl;
  trace.info() << "|K2-K2_CNC|_2  = " << error_K2_l2 << std::endl;

  // Remove normals for better blocky display.
  smesh.vertexNormals() = SH::RealVectors();
  smesh.faceNormals()   = SH::RealVectors();
  typedef SurfaceMeshWriter< RealPoint, RealVector > SMW;
  const double    Kmax = std::max( fabs( *exp_K1_min_max.first ),
                                   fabs( *exp_K2_min_max.second ) );
  const auto colormapK1 = makeQuantifiedColorMap( makeColorMap( -Kmax, Kmax ) );
  const auto colormapK2 = makeQuantifiedColorMap( makeColorMap( -Kmax, Kmax ) );
  auto colorsK1 = SMW::Colors( smesh.nbFaces() );
  auto colorsK2 = SMW::Colors( smesh.nbFaces() );
  for ( auto i = 0; i < smesh.nbFaces(); i++ )
    {
      colorsK1[ i ] = colormapK1( K1[ i ] );
      colorsK2[ i ] = colormapK2( K2[ i ] );
    }
  SMW::writeOBJ( "example-cnc-K1", smesh, colorsK1 );
  SMW::writeOBJ( "example-cnc-K2", smesh, colorsK2 );
  const auto avg_e = smesh.averageEdgeLength();
  SH::RealPoints positions( smesh.nbFaces() );
  for ( auto f = 0; f < positions.size(); ++f )
    {
      D1[ f ] *= smesh.localWindow( f );
      positions[ f ] = smesh.faceCentroid( f ) - 0.5 * D1[ f ];
    }
  SH::saveVectorFieldOBJ( positions, D1, 0.05 * avg_e, SH::Colors(),
                          "example-cnc-D1",
                          SH::Color::Black, SH::Color( 0, 128, 0 ) );
  for ( auto f = 0; f < positions.size(); ++f )
    {
      D2[ f ] *= smesh.localWindow( f );
      positions[ f ] = smesh.faceCentroid( f ) - 0.5 * D2[ f ];
    }
  SH::saveVectorFieldOBJ( positions, D2, 0.05 * avg_e, SH::Colors(),
                          "example-cnc-D2",
                          SH::Color::Black, SH::Color(128, 0,128 ) );
  return 0;
}